Anytime an important New Yorker leaves behind a nice home, real estate agents wonder aloud about how they might nab the listing. “You find out who the estate attorney is,” the director of Stribling Private Brokerage once said, “and you write them.”

After Walter Cronkite died this July at age 92, it was sad to think that brokers would be clamoring for an apartment that had belonged to someone with such cosmic grace and gravitas. But there won’t be a clamor. Joanna Simon, a vice president at the boutique brokerage Fox Residential, and Cronkite’s companion during the last four years, will be listing his UN Plaza co-op within the month for $2,995,000.

Ms. Simon, 68, became a broker in the 1990s. “Liz Smith, who was a friend,” she said, “put something in her column about the fact that Joanna Simon, former opera singer and TV star—because, you know, I worked for PBS—has started a new career, and she’s hot.” (She had been an arts correspondent and a mezzo-soprano, though it was sister Carly who wrote “You’re So Vain”; their father, Richard, co-founded Simon & Schuster.)

The tennis player Ham Richardson, and his wife, Midge, a past editor of Seventeen, read the announcement. “They called me, and said, ‘We have this fabulous apartment we would like to sell.’” It was at 860/870 UN Plaza, the mid-1960s towers where Truman Capote once lived and where Ms. Simon happened to have a place, too.

The Cronkites were looking for a new apartment with Ms. Simon’s boss, Barbara Fox, but weren’t interested in moving near the United Nations. “I said, ‘Let’s hire a very fancy car, and put blinders on,’” Ms. Simon said. The couple came, but a fog made it hard to appreciate the massive East River views. “They could not see out the apartment, but they loved the layout. And they bought it.”

After a small fight over wall sconces, she said, the deal closed. “Betsy—Mrs. Cronkite—and I became good friends; and Walter and my husband, Gerald Walker, who had been an editor for The New York Times, had a lot in common.” By the end of 2005, after the deaths of their spouses, the broker and the anchor were keeping company, as he once put it.

Ms. Simon, who has kept her original co-op in the building, said that a buyer may want to update the kitchen and bathrooms in Cronkite’s apartment, or change it back from a two-bedroom to a four-bedroom. “It has an early American look, and that’s not very fashionable these days. When he saw my apartment, he said, ‘I would love to live here, but it’s so feminine. We’d have to bring in a lot of masculine things.’ He has leather chairs and big desks, and a lot of big couches and things like that. It looked like Walter.”